Elastic and Thermoelastic Responses of Orthotropic Half-Planes

A unified approach is presented for constructing explicit solutions to the plane elasticity and thermoelasticity problems for orthotropic half-planes. The solutions are constructed in forms which decrease the distance from the loaded segments of the boundary for any feasible relationship between the elastic moduli of orthotropic materials. For the construction, the direct integration method was employed to reduce the formulated problems to a governing equation for a key function. In turn, the governing equation was reduced to an integral equation of the second kind, whose explicit analytical solution was constructed by using the resolvent-kernel algorithm.

Gaussian Local Phase Approximation in a Cylindrical Tissue Model

In NMR or MRI, the measured signal is a function of the accumulated magnetization phase inside the measurement voxel, which itself depends on microstructural tissue parameters. Usually the phase distribution is assumed to be Gaussian and higher-order moments are neglected. Under this assumption, only the x-component of the total magnetization can be described correctly, and information about the local magnetization and the y-component of the total magnetization is lost. The Gaussian Local Phase (GLP) approximation overcomes these limitations by considering the distribution of the local phase in terms of a cumulant expansion. We derive the cumulants for a cylindrical muscle tissue model and show that an efficient numerical implementation of these terms is possible by writing their definitions as matrix differential equations. We demonstrate that the GLP approximation with two cumulants included has a better fit to the true magnetization than all the other options considered. It is able to capture both oscillatory and dampening behavior for different diffusion strengths. In addition, the introduced method can possibly be extended for models for which no explicit analytical solution for the magnetization behavior exists, such as spherical magnetic perturbers.

Finite element simulation of ductile fracture in polycrystalline materials using a regularized porous crystal plasticity model

In the present study, a hypoelastic–plastic formulation of porous crystal plasticity with a regularized version of Schmid’s law is proposed. The equation describing the effect of the voids on plasticity is modified to allow for an explicit analytical solution for the effective resolved shear stress. The regularized porous crystal plasticity model is implemented as a material model in a finite element code using the cutting plane algorithm. Fracture is described by element erosion at a critical porosity. The proposed model is used for two test cases of two- and three-dimensional polycrystals deformed in tension until full fracture is achieved. The simulations demonstrate the capability of the proposed model to account for the interaction between different modes of strain localization, such as shear bands and necking, and the initiation and propagation of ductile fracture in large scale polycrystal models with detailed grain description and realistic boundary conditions.

A Numerical and Analytical Study of Phase Synchronization in Coupled SC-CNN Based Non-Identical Chaotic Systems

This paper seeks to address the phase synchronization phenomenon using the drive-response concept, in our proposed model, State Controlled Cellular Neural Network (SC-CNN) based on variant of MuraliLakshmanan-Chua (MLCV) circuit. Using this unidirectionally coupled chaotic non autonomous circuits, we described the transition of unsynchronous to synchronous state, by numerical simulation method as well as the results are confirmed by solving explicit analytical solution. In this aspect, the system undergoes the new effect of phase synchronization (PS) phenomenon have been observed before complete synchronization (CS) state. To characterize these phenomena by the phase portraits and the time series plots. Also particularly characterize for PS by the method of partial Poincare section map using phase difference versus time, numerically and analytically. The study of dynamics involved in SC-CNN circuit systems, mainly applicable in the field of neurosciences and in telecommunication fields.

Analytical solutions of incommensurate fractional differential equation systems with fractional order $ 1 < \alpha, \beta < 2 $ via bivariate Mittag-Leffler functions

<abstract><p>In this paper, we derive the explicit analytical solution of incommensurate fractional differential equation systems with fractional order $ 1 &lt; \alpha, \beta &lt; 2 $. The derivation is extended from a recently published paper by Huseynov et al. in ^{[<xref ref-type="bibr" rid="b1">1</xref>]}, which is limited for incommensurate fractional order $ 0 &lt; \alpha, \beta &lt; 1 $. The incommensurate fractional differential equation systems were first converted to Volterra integral equations. Then, the Mittag-Leffler function and Picard's successive approximations were used to obtain the analytical solution of incommensurate fractional order systems with $ 1 &lt; \alpha, \beta &lt; 2 $. The solution will be simplified via some combinatorial concepts and bivariate Mittag-Leffler function. Some special cases will be discussed, while some examples will be given at the end of this paper.</p></abstract>

Boundary problem on semi-direct for pseudoparabolic equation with a small parametr

Данная статья посвящена построению классического решения краевой задачи на полупрямой для линейного псевдопараболического уравнения с малым параметром. Для построения явного решения используется метод преобразование Фурье. В работе исследуется вопрос об однозначной разрешимости начально-краевой задачи для псевдопараболического уравнения с малым параметром на полуоси. Получено явное аналитическое решение поставленной задачи. In this paper, we study the question of the unique solvability of the initial-boundary-value problem for a pseudoparabolic equation with a small parameter on the semi-axis. An explicit analytical solution to the problem is obtained.

Linear processes on complex networks

This article studies the dynamics of complex networks with a time-invariant underlying topology, composed of nodes with linear internal dynamics and linear dynamic interactions between them. While graph theory defines the underlying topology of a network, a linear time-invariant state-space model analytically describes the internal dynamics of each node in the network. By combining linear systems theory and graph theory, we provide an explicit analytical solution for the network dynamics in discrete-time, continuous-time and the Laplace domain. The proposed theoretical framework is scalable and allows hierarchical structuring of complex networks with linear processes while preserving the information about network, which makes the approach reversible and applicable to large-scale networks.